# Project #8233 - Algebra

Eleven Algebra problems (see below) - that should be completed in the attached Word document

1. (10 pts) Look at the graphs in exercises #44, 48, 64, 65, 67 on page 89 in section 1.2.

For each graph, does it represent a one-to-one function?  (Yes or No?) (no explanation required)

#44_______            #48________          #64_______         #65_______     #67_______

2.  (6 pts) A contagious disease is infecting residents of a town of 8,700 residents.

The number of residents infected t days after the disease has begun is given by the function

How many residents have been infected with the disease 15 days after the disease has begun?

(no explanation required)                                                                       2. _______

A.             17

B.        3,885

C.        7,006

D.        8,500

3.  (6 pts)  \$14,000 is invested in an account paying 4.2% annual interest compounded quarterly.

Find the amount of money in the account at the end of 12 years.

(Use the compound interest formula found in Example 4 on page 404.)                         3. _______

(explanation optional)

A.     \$21,056.00

B.     \$22,937.00

C.     \$23,118.80

D.   \$100,873.80

4. (6 pts)  Convert to a logarithmic equation: 9x = 729.      (explanation optional)                  4. ______

A.

B.

C.

D.

5. (6 pts)  Which of the following expressions is equal to ?                 5. ______

(explanation optional)

A.       log (3/2) + log x +  log y – log z

B.       log 2 + 3 log x + (1/2) log y  – 2 log z

C.       log  [6x + (1/2)y – 2z ]

D.

6. (6 pts) The average walking speed w, in feet per second, of a person living in a city of population P, where P is measured in thousands, is given by the function w(P) = 0.37 ln P + 0.05

The population of Center City is 360,000. Find the average walking speed.                6. _______

(explanation optional)

A.     1.0 ft/sec

B.     2.1 ft/sec

C.     2.2 ft/sec

D.     4.8 ft/sec

7.  (6 pts) Use a calculator (standard scientific calculator or an online graphing calculator) to find each of the following numerical values. Write your answer rounded to 4 decimal places (i.e., the nearest ten thousandth).

(a)  6 –2.3

(b)  e 0.45

8. (10 pts)

(a)       _______  (fill in the blank)

For parts b and c, let.

(b)   Write the exponential form of the equation.

(c)    Determine the numerical value of x, in simplest form.

9. (10 pts) Use composition of functions to show that the functions

and    are inverse functions.

That is, carefully show that  and show that .

10. (16 pts)  Let

(a)  Find the inverse function of f.  Show work.

(b) What is the domain of f ? What is the domain of the inverse function?

11. (18 pts) Let f(x) = 3 + ex  .

(a) Which describes how the graph of f can be obtained from the graph of y = ex ?    Choice: ________

A.     Reflect the graph of y = exacross the y-axis and shift upward by 3 units.

B.     Reflect the graph of y = exacross the x-axis and shift upward by 3 units.

C.     Shift the graph of  y = ex  to the right by 3 units and shift downward by 1 unit.

D.     Shift the graph of  y = ex  to the left by 1 unit and shift upward by 3 units.

(b) What is the y-intercept?

(c) What is the domain of f ?

(d) What is the range of f ?

(e) What is the horizontal asymptote?

(f) Which is the graph of f ?

GRAPH A                                 GRAPH B                                              GRAPH C

 Subject Mathematics Due By (Pacific Time) 06/28/2013 05:00 pm
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